Sub-Resolution Assist Features (SRAFs) are used in optical lithography to improve the manufacturing process window (PW). They are added to the mask shapes to create a denser environment that improves the printability of the target design shapes on wafer. As the critical dimensions (CDs) that need to be patterned shrink with every technology generation, SRAFs have become a critical and key component in enabling processes with manufacturable process windows. The size and placement of the SRAFs must be carefully optimized to provide the maximum benefit to the main feature while avoiding any printing on resist that could affect subsequent etching processes. The un-intended printing of assist features on wafer is a critical yield detractor and is especially pervasive in newer technology nodes, where more aggressive and more complex SRAF patterns and placement are becoming commonplace. The need for the accurate prediction of SRAF printing is therefore very important to achieve the maximum main feature process window benefit without any assist feature printing.Traditionally, the optimization of SRAF sizing and placement consisted of a set of rules obtained through the extensive analysis of wafer printability on a variety of assisted mask patterns while using Scanning Electron Microscope images of the resist surface to monitor unwanted SRAF printing. Recent advances in model-based assist feature optimization methods allow for the automated adjustment of both main feature and assist feature size and placement through simulation of the aerial image, but critically rely on the accuracy of the lithography process model to ensure non-printing of the SRAF. Lithography or Optical Proximity Correction (OPC) models usually comprising an optical and a resist model are calibrated to measurements of the resist bottom CD. These models are naturally better at predicting the printing of SRAFS that are lines in resist. When the SRAFs are holes in resist, for eg. assist features supporting main features on a dark field mask, or SRAFs supporting inverse tone features on a bright field mask, these models do not have the required accuracy in predicting SRAF printing. SRAF printability prediction has thus far been tackled by large dose adjustments to the OPC model, to match simulation to wafer results. The drawbacks of this method have been two-fold -simple dose adjustments do not accurately predict printing across various SRAF configurations and the main feature printability is compromised We present in this paper a method to calibrate and predict printing of assist features that appear as a dimpling in the resist surface, by carefully selecting the calibration data and separately tuning the model parameters for the main feature and of the SRAF printing models. With this method, we obtain a model that accurately predicts the printing of various configurations of SRAFs on wafer while still maintaining the accuracy on the main features. An analysis of the implementation of such a model in the OPC flow and the corresponding supporting results ...

In this paper, a new notion, namely fuzzification of PMS-algebra, a generalization of BCK/BCI/TM/KUS/PS-algebras is initiated along with fuzzified PMSideal and discussed some of its properties in detail.

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Abstract. This paper introduces some simple properties and theorem based on fuzzy trident distance along with the help of trapezoidal fuzzy numbers. The results are discussed along with suitable illustrative example.